$\vec u = 5\hat i +3\hat j$ Find the direction angle of $\vec u$. Enter your answer as an angle in degrees between $0 ^\circ$ and $360^\circ$ rounded to the nearest hundredth. $\theta =$
Solution: What is a direction angle? The direction angle, $\theta$, of $\vec{u}$ is the angle between the positive $x$ -axis and $\vec{u}$. $y$ $x$ $(5, 3)$ $\vec u$ $\theta$ Using the inverse tangent function Let's think about the components of $\vec u$ and use the inverse tangent function, $\tan^{-1}$ (also sometimes called arctangent and written as $\arctan$ or $\text{atan}$ ) to find $\theta$. $y$ $x$ $(5, 3)$ $\vec u$ $\theta$ $3}$ $5}$ $\theta = \text{tan}^{-1} \left ( \dfrac{\text{Vertical component}}{\text{Horizontal component}} \right) ~~~$ $\theta=\text{tan}^{-1}\left(\dfrac{3}{5}\right)$ $\theta\approx{30.96^\circ}$ This makes sense because ${30.96^\circ}$ is in the first quadrant, and $\vec u$ is in the first quadrant. The answer $\theta \approx 30.96^\circ$